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Shock tubes are used to investigate the chemical kinetics and radiative properties of gasses. Analyses of the flow conditions produced in shock tubes typically assume a single, constant shock speed...

A two dimensional fully nonlinear numerical wave flume is extended with a pneumatic model to compute the free surface flow inside the chamber of land-based Oscillating Water Column (OWC) devices. Potential theory and the Mixed Eulerian-Lagrangian method are employed to compute the fluid flow using the direct Boundary Element Method (BEM) enhanced by a non-uniform rational B-Spline function. Meanwhile, a pneumatic model is manipulated to obtain the instantaneous air pressure on the chamber's free surface. Spring-like behavior of a perfect gas through an adiabatic process and a linear power take-off mechanism are used in the pneumatic model that makes time derivative of the air pressure turns to a function of reciprocating air and fluid flows in the chamber. Therefore, temporary air pressure is taken into account on the fully nonlinear free surface boundary conditions implicitly along with the time marching algorithm. The hydrodynamic efficiency of an OWC interacting with second-order Stokes waves is compared with former studies to verify the present model. To assess the present model for simulating the air compressibility in a large-scale case study, the present solution is compared with experimental and mathematical results under an irregular wave. Afterwards, an OWC device is exposed to fifth-order Stokes waves in the flume to examine the numerical stability of computing the free surface flow outside and inside of the chamber.

This wok focuses to develop a numerical computation program allowing to design new contours of a supersonic nozzle having several bells, adapted to several levels of different altitudes, going from sea level and progressively with the altitude up to space, giving a supersonic uniform and parallel flow to the exit section and a maximum possible thrust without loss, aiming to reduce considerably the side loads caused in the conventional and the dual bell nozzles when the ambient pressure decrease with the altitude. The first bell has a sonic, uniform and parallel inlet to the throat, and a sea level adaptation with a reduced supersonic Mach number, while the other bell have a supersonic, parallel and uniform inlet and an adaptation to a given altitude with a progressed increase of supersonic Mach number. The transition from one level of adaptation to another adjacent is done without mechanical activation. The purpose of this type of nozzle is to have the possibility of flying in several supersonic regimes adapted to several different altitudes with a reduced side loads. This type of nozzle is named by Several Bell Nozzle and has inflection points between bell and adjacent other. The design is done in the context of a calorically and thermally perfect gas. The problem is to design a typical bell having a uniform and parallel supersonic inlet and exit with two given Mach numbers. The design is made by the use of the Method of Characteristics. The resolution of the equations is done numerically by the finite difference corrector predictor algorithm. The validation of the results is controlled by the convergence of the ratio of the critical sections, calculated numerically, to that given by the theory. In this case, all the design parameters converge automatically to the desired solution. The application is made for axisymmetric MLN having 3, 4, 5 and 10 bells.

Convection has been discussed in the field of accretion discs for several decades, both as a means of angular momentum transport and also because of its role in controlling discs' vertical structure via heat transport. If the gas is sufficiently ionized and threaded by a weak magnetic field, convection might interact in non-trivial ways with the magnetorotational instability (MRI). Recently, vertically stratified local simulations of the MRI have reported considerable variation in the angular momentum transport, as measured by the stress to thermal pressure ratio $\alpha$, when convection is thought to be present. Although MRI turbulence can act as a heat source for convection, it is not clear how the instabilities will interact dynamically. Here we aim to investigate the interplay between the two instabilities in controlled numerical experiments, and thus isolate the generic features of their interaction. We perform vertically stratified, 3D MHD shearing box simulations with a perfect gas equation of state with the conservative, finite-volume code PLUTO. We find two characteristic outcomes of the interaction between the two instabilities: straight MRI and MRI/convective cycles, with the latter exhibiting alternating phases of convection-dominated flow (during which the turbulent transport is weak) and MRI-dominated flow. During the latter phase we find that $\alpha$ is enhanced by nearly an order of magnitude, reaching peak values of $\sim 0.08$. In addition, we find that convection in the non-linear phase takes the form of large-scale and oscillatory convective cells. Convection can also help the MRI persist to lower Rm than it would otherwise do. Finally we discuss how our results help interpret simulations of Dwarf Novae., Comment: Accepted for publication in MNRAS (23 pages, 14 figures, 1 table)

When gas flows at a high speed in a channel with a variable cross sectional area and high-intensity energy supply, it experiences complicated physical and chemical processes producing high-temperature gas effects. High-temperature gas effects are a key issue related to design and optimization of nozzles of plasmatron of alternating current. The finite volume method is applied to solve unsteady compressible Euler equations with high-temperature gas effects. Solutions of some benchmark test cases are reported, and comparison between computational results of chemically equilibrium and perfect air flowfields is performed. The results of numerical simulation of one-dimensional and two-dimensional under- and over-expanded nozzle flows with a moving region of energy supply are presented. Output nozzle parameters are calculated as functions of a number and time of burning of plasmatron arcs. The results obtained show a qualitative pattern of gas dynamics and thermal processes in the nozzle with unsteady energy supply demonstrating the displacement of the nozzle shock wave towards the nozzle outlet in the over-expanded nozzle flow in comparison to perfect gas flow.

A compressible supersonic turbulent jet of a perfect gas in a co-flow with the formulation of stochastic spectral inflow boundary conditions is numerically modeled. The base equations are the LES averaged Navier – Stokes equations closed by the Smagorinsky model, the solution of which is carried out by the ENO scheme of the third order of accuracy. The stochastic boundary conditions at the inlet are constructed on the basis of the spectral method of generating fluctuations of gas-dynamic variables to obtain an inhomogeneous anisotropic turbulent flow. The numerical results of turbulent characteristics are compared with experimental data for the shear layer problem. The thickness of the shear layer is obtained, in which the growth of the shear layer between the jet and the co-flow for three types of grid (coarse, medium and fine) is demonstrated. Coherent vortex structures appearing in the jet are constructed in dynamics, which made it possible to analyze in detail the growth and development of vortices over time.

Numerical simulations of 3-D disturbances induced by an underexpanded jet in supersonic crossflow (JISC) in the Mach 5.4 flat-plate boundary layer (BL) are carried out. The Navier–Stokes equations for compressible perfect gas are integrated using the in-house solver implementing an implicit finite-volume shock-capturing scheme with the second-order approximation in space and time. The numerical solutions indicate that the wall normal injection through a circular hole forms an underexpanded jet of barrel shape, which induces a system of vortices propagating downstream. These vortices are destabilized at a short distance that leads to rapid nonlinear breakdown and formation of a turbulent wedge. The vortex structure, its instability and breakdown to turbulence resemble those induced by an isolated roughness element. It is shown that the normal wall injection effectively trips the BL flow. This encourages further numerical studies of active tripping of high-speed BL flows using rows of JISC.

In a recent publication, Hornung et al. (J. Fluid Mech., vol. 871, 2019, pp. 1097–1116) showed that the shock wave stand-off distance and the drag coefficient of a cone in the inviscid hypersonic flow of a perfect gas can be expressed as the product of a function of the inverse normal-shock density ratio ε and a function of the cone-angle parameter η, thus reducing the number of independent parameters from three (Mach number, specific heat ratio and angle) to two. Analytical forms of the functions were obtained by performing a large number of Euler computations. In this article, the same approach is applied to a symmetrical flow over a wedge. It is shown that the same simplification applies and corresponding analytical forms of the functions are obtained. The functions of ε are compared with the newly determined corresponding functions for flow over a circular cylinder.

The aim of this work is to develop a calculation model based on the method of characteristics making it possible to study the effect of the stagnation pressure of the combustion chamber on the 2D and axisymmetric minimum length nozzle design giving a uniform and parallel flow at the exit section. The model is based on the use of the real gas approach. The co-volume and the intermolecular interaction effect are taken into account by the use of the Berthelot state equation. The effect of molecular vibration is considered in our model to evaluate the behaviour of gas at a high temperature. In this case, the stagnation pressure and the stagnation temperature are important parameters in our model. The resolution of the algebraic equations is done by the finite difference corrector predictor algorithm. The validation of the results is controlled by the convergence of the critical section ratios calculated numerically as obtained by the theory. The mass and the thrust are evaluated to improve the efficiency of the nozzle. The comparison is made with the high temperature and perfect gas models. The application is made for air.

The development of inviscid and viscous two-dimensional subsonic disturbances in the supersonic flat-plate boundary layer of a vibrationally excited gas is investigated on the basis of the linear stability theory. The system of two-temperature gas dynamics which includes the Landau-Teller relaxation equation is used as the initial model. Undisturbed flow is described by the self-similar boundary-layer solution for a perfect gas. It is shown that in the inviscid approximation excitation decreases the maximum growth rate of the most unstable second mode by 10–12% as compared with an ideal gas. The neutral stability curves are calculated for the first and second most unstable modes at the Mach numbers M = 2.2, 4.5, and 4.8. For both modes the critical Reynolds numbers at maximum excitation are greater by 12–13% than the corresponding values for the perfect gas.

A new framework, Eigen Analysis in General Curvilinear Coordinates (EAGCC), is presented for internal propagation of linear acoustic flow disturbances through irregular but smoothly varying duct geometries and non-uniform but smoothly varying mean flows. The framework is based on an eigen analysis of the linearised Euler equations for a perfect gas formulated in a general curvilinear coordinate system. A series of test cases are studied, from a simple uniform cylindrical annular duct with uniform mean flow to an axially and circumferentially non-uniform duct with non-uniform mean flow, which together validate the method for acoustic propagation through non-uniform annular ducts and non-uniform but irrotational and homentropic mean flow: although the framework provides for rotational and non-homentropic mean flow, and for modelling vortical and entropic flow perturbations, these features are not validated in this paper. Two propagation methods are presented. The first is a one-way “single sweep” calculation, in which only information travelling in the direction of propagation is retained. The second is an iterative “two-way sweep” method that accurately captures reflected waves and returns transmitted and reflected perturbations. Previous eigenvector analyses were subject to limitations on geometry and mean flow (for instance slowly-varying ducts) that are not required in the current method, for which the only limitations are that the duct and mean flow vary smoothly with position. This work extends the scope of the eigenvector approach to include acoustic problems previously limited to volumetric or surface-based methods.

The presented results of computations of the aerodynamic and acoustic characteristics of an isolated symmetric NACA0012 airfoil with a blunt trailing edge in a subsonic homogeneous viscous perfect gas flow at zero angle of attack are obtained using the MP5 modified finite-difference scheme proposed in this study. The computations are accomplished within the zonal RANS–IDDES approach engaging the basic RANS Spalart–Allmaras model. A synthetic turbulence generator with a three-dimensional source is used to create turbulent content at the entrance to the IDDES domain. A series of model problems are considered, whose solutions allowed tuning the parameters of the proposed difference scheme and solving some methodological problems related to processing the simulation results.

The aim of this paper is to numerically analyze the energy separation phenomenon in turbulent compressible swirling flow in a cylindrical tube. In that sense, the energy separation in a vortex tube with orifice at cold end closed completely is examined numerically using OpenFOAM software. Obtained results are validated with the experimental ones. For numerical calculations, both two-equation (standard k-ε) and full Reynolds stress turbulence models (LRR) are used. The computational domain is considered to be two-dimensional, and the working fluid - air is treated as calorically perfect gas. Mesh independence test is carried out for four different mesh sizes. Distributions of swirling flow intensity, average swirl and angular velocity clearly show the influence of the swirl presence in the flow. The values of these quantities point to the physics of this extremely complex flow-thermodynamic phenomenon, such is the energy separation. Based on values and distributions of these flow quantities a comparison between incompressible and compressible turbulent swirling flow is performed.

To study the Reynolds stress budgets, direct numerical simulations of high-temperature supersonic turbulent channel flow for thermally perfect gas and calorically perfect gas are conducted at Mach number 3.0 and Reynolds number 4800 combined with a dimensional wall temperature of 596.30 K. The reliability of the direct numerical simulation data is verified by comparison with previous results ( J Fluid Mech 1995, vol. 305, pp.159–183). The effects of variable specific heat are important because the vibrational energy excited degree exceeds 0.1. The viscous diffusion, pressure–velocity gradient correlation, and dissipation terms in the Reynolds stress budgets for TPG, except the streamwise component, are larger than those for calorically perfect gas close to the wall. Compressibility-related term decreases when thermally perfect gas is considered. The major difference for both gas models is mainly due to variations in mean flow properties. Inter-component transfer related to pressure–velocity gradient correlation term can be distinguished into inner and outer regions, whose critical position is approximately 16 for both gas models.

The noise of jet and rocket engines involves the coupling of sound to swirling flows and to heat exchanges leading in the more complex cases of triple interactions to acoustic-vortical-entropy (AVE) waves. The present paper presents the derivation of the AVE equation for axisymmetric linear non-dissipative, compressible perturbations of a non-homentropic, swirling mean flow, with constant axial velocity and constant angular velocity for a perfect gas with constant density. The axisymmetric AVE wave equation is obtained for the radial velocity perturbation, specifying its radial dependence for any frequency and axial wavenumber. The AVE wave equation in the case of zero axial wavenumber, corresponding to cylindrical AVE waves, has no singularities for finite radius, including the sonic radius, where the isothermal Mach number for the swirl velocity is unity. The exact solution of the AVE wave equation for the fundamental axisymmetric mode with zero axial wavenumber is obtained without any restriction on frequency, as series expansions of Gaussian hypergeometric type: (i) covering the whole flow region; (ii) specifying the wave field at the sonic radius; (iii) specifying near-axis and asymptotic scaling for small and large radius. Using polarization relations among wave variables specifies exactly and allows the plotting of the perturbations of: (i,ii) the radial and azimuthal velocity; (iii,iv) pressure and mass density; (v,vi) entropy and temperature. Thus the extension of cylindrical acoustic waves, that are specified by Bessel functions, to cylindrical acoustic-vortical-entropy waves, is specified by Gaussian hypergeometric functions.

Direct numerical simulations of temporally evolving supersonic turbulent channel flow of thermally perfect gas are conducted at Mach number 3.0 and Reynolds number 4800, combined with constant dime...

It is known from the literature that Large Eddy Simulations of dense gas flows can prove very useful in order to better understand the behavior of friction losses in Organic Rankine Cycle turbines and expanders. Yet, no dedicated turbulence closure models exist for such flows. In this study, the authors lay the fondations for the development of turbulence closure models in dense gas flows. The Subgrid-Scale terms are first rigorously derived from the filtered Navier-Stokes equations. Additional terms to the well-known Subgrid-Scale closure terms are identified in the dense gas context. Using Direct Numerical Simulation, the variances of Subgrid-Scale terms in the filtered momentum equations are computed both for the dense and perfect gas cases and significant differences are revealed between the two cases. A model using only filtered fields as input is derived for one of the dense gas specific Subgrid-Scale terms using a Correlation Patterns Modeling approach. Preliminary a priori tests indicate that this approach can be easily implemented and provides promising results.

For a successful space programme, the reusable spacecraft should survive numerous re-entry conditions. The re-entry of almost all the reusable space shuttles resembles a flat plate at high angles of attack because of its flat windward surface. The feasibility of concave ventral surface in space shuttles is analysed computationally with a commercially available solver scFLOW. A full three-dimensional Navier–Stokes equations are solved over a thin concave plate at different angles of attack to a hypersonic flow. The peak temperature and drag coefficients of different eccentric plates are compared with that of a flat plate normal to the flow. The air is assumed to be thermally perfect gas. The flow is assumed to be continuum. The total heat transfer rates and peak heat fluxes of a concave plate are compared with the flat plate. This paper discusses the results of these simulations and how the concavity behaves in the re-entry of spacecraft.

The performance of a rotatable Pitot cylinder probe was experimentally investigated in the calibration test section of a closed loop organic vapor wind tunnel with the working fluid Novec™ 649 at elevated density level. Subsonic up to high subsonic flow conditions (M = 0.5 – 0.7) were covered by the experiments. The data reduction process for obtaining Mach numbers and velocity based on non-ideal flow calculations and corresponding isentropic relations were reviewed. The theoretical results were compared with experimental data. It was found that in the case of high subsonic non-ideal gas flows, significant deviations in comparison with conventional perfect gas flows occurred.

In this work, natural convection and temperature distribution of supercritical water in a side-wall heated cavity are studied by numerical simulation. Different from ordinary single-vortex flow of perfect gas, supercritical water shows a thinner boundary layer with much higher velocity and finally forms a double-vortex natural convection pattern in the cavity. Moreover, for supercritical water, the temperature near the top wall of the cavity will exceed that of the heating wall, which is called overheating. Temperature, pressure, temperature difference between wall and fluid and aspect ratio will all affect velocity and temperature in the cavity. The mechanism analysis shows that the unique physical properties of supercritical water are vital reasons affecting the buoyancy driven flow boundary layer. The strong flow boundary layer will further lead to double-vortex flow pattern and overheating phenomenon, which will also affect natural convection pattern and temperature distribution.

A generic solver in a structured Cartesian adaptive mesh refinement framework is extended to simulate unsteady shock-induced combustion problems on a structured curvilinear mesh. A second-order accurate finite volume method is used with a grid-aligned Riemann solver for inviscid thermally perfect gas mixtures. To solve these reactive problems, detailed chemical kinetic mechanisms are employed with a splitting approach. The prolongation and restriction operators are modified to implement the adaptive mesh refinement algorithm on a mapped mesh. The developed solver is verified with several benchmark tests and is then used to simulate unsteady shock-induced combustion. The results show that the computed stand-off distance of waves and oscillation frequencies of mass fraction of products observed at the stagnation point are in good agreement with the results from experiments.

Large wave drag and high surface heating are common problems encountered at hypersonic speeds and these should be properly dealt for the effective and safe flights. Many studies have been carried out to mitigate these problems by employing various active and passive techniques but most of these computational or experimental studies account lower stagnation enthalpy flows or perfect gas assumption. Hence the current study examines the effect of higher freestream stagnation enthalpy on flow field alteration for counter - jet drag reduction technique for a hemispherical object. Results also includes the real gas effects on flow field, wave drag and wall heat flux. Further the effect of various flow parameters is observed on surface pressure distribution, surface heat flux and drag force for the hypersonic flow over the hemisphere, using the in house developed perfect gas and non - equilibrium N - S flow solvers. Results reveal that the perfect gas assumption overestimates surface properties and wave drag value. Drag coefficient reduces with freestream total enthalpy ( H o ) in the presence of real gas effects. Around 30% drag reduction is observed at H o =1 MJ/kg for Mach number 5 as compared to no - jet case and this reduction increases at higher freestream total enthalpy for same injection pressure ratio. Higher pressure ratio of the jet results in lower surface pressure and Stanton number on the object which gives lower wave drag.

A study of dense-gas effects on the laminar, transitional and turbulent characteristics of boundary layer flows is conducted. The laminar similarity solution shows that temperature variations are small due to the high specific heats of dense gases, leading to velocity profiles close to the incompressible ones. Nevertheless, the complex thermodynamics of the base flow has a major impact on unstable modes, which bear similarities with those obtained for a strongly cooled wall. Numerical simulations of spatially developing boundary layers yield turbulent statistics for the dense gas flow that remain closer to the incompressible regime than perfect gas ones despite the presence of strongly compressible structures.

High-speed turbulent boundary layers of a dense gas (PP11) and a perfect gas (air) over flat plates are investigated by means of direct numerical simulations and large eddy simulations. The thermodynamic conditions of the incoming flow are chosen to highlight dense gas effects, and laminar-to-turbulent transition is triggered by suction and blowing. In the paper, the behavior of the fully developed turbulent flow region is investigated. Due to the low characteristic Eckert number of dense gas flows ( $$\hbox {Ec}=U_\infty ^2/c_{p,\infty }T_\infty$$ ), the mean velocity profiles are largely insensitive to the Mach number and very close to the incompressible case even at high speeds. Second-order velocity statistics are also weakly affected by the flow Mach number and the velocity spectra are characterized by a secondary peak in the outer region of the boundary layer because of the higher local friction Reynolds number. Despite the incompressible-like velocity and Reynolds-stress profiles, the strongly non-ideal thermodynamic and transport-property behavior of the dense gas results in unconventional distributions of the fluctuating thermo-physical quantities. Specifically, density and viscosity fluctuations reach a peak close to the wall, instead of vanishing as in perfect gas flows. Additionally, dense gas boundary layers exhibit higher values of the fluctuating Mach number and velocity divergence and a larger dilatational-to-solenoidal dissipation ratio in the near-wall region, which represents a major deviation from high-Mach-number perfect gas boundary layers. Other significant deviations are represented by the more symmetric probability distributions of fluctuating quantities such as the density and velocity divergence, due to the more balanced occurrence of strong expansion and compression events.

This chapter will describe the extensions of the AUSM-family fluxes (specifically, SLAU2) to real fluids of multiphase flows, supercritical fluids, and magnetohydrodynamics (MHD), where the governing equations and/or their discretizations differ from those for the perfect gas. These fluids are of great importance to physics and industries, but call for special care due to the changes in the equations. Some readers may wonder why the author appears to have a preference for the AUSM family. Here is a list of primary reasons: 1. They are robust and accurate for resolving shock waves at high speeds. 2. All-speed variants (e.g., AUSM+-up, SLAU2) are available that are applicable to low speeds. 3. No differentiation of a flux function or its Eigenstructure is required, which allows its straightforward application to the complex equation-of-state (EoS) of multiphase flows, supercritical fluids, or MHD.

The aim of this work is to develop a new numerical calculation program to determine the effect of the stagnation temperature on the calculation of the supersonic flow around a pointed airfoils using the equations for oblique shock wave and the Prandtl Meyer expansion, under the model at high temperature, calorically imperfect and thermally perfect gas, lower than the dissociation threshold of the molecules. The specific heat at constant pressure does not remain constant and varies with the temperature. The new model allows making corrections to the perfect gas model designed for low stagnation temperature, low Mach number, low incidence angle and low airfoil thickness. The stagnation temperature is an important parameter in our model. The airfoil should be pointed at the leading edge to allow an attached shock solution to be seen. The airfoil is discretized into several panels on the extrados and the intrados, placed one adjacent to the other. The distribution of the flow on the panel in question gives a compression or an expansion according to the deviation of the flow with respect to the old adjacent panel. The program determines all the aerodynamic characteristics of the flow and in particular the aerodynamic coefficients. The calculation accuracy depends on the number of panels considered on the airfoil. The application is made for high values of stagnation temperature, Mach number and airfoil thickness. A comparison between our high temperature model and the perfect gas model is presented, in order to determine an application limit of the latter. The application is for air.

Dense gas effects, encountered in many engineering applications, lead to unconventional variations of the thermodynamic and transport properties in the supersonic flow regime, which in turn are responsible for considerable modifications of turbulent flow behavior with respect to perfect gases. The most striking differences for wall-bounded turbulence are the decoupling of dynamic and thermal effects for gases with high specific heats, the liquid-like behavior of the viscosity and thermal conductivity, which tend to decrease away from the wall, and the increase of density fluctuations in the near wall region. The present work represents a first attempt of quantifying the influence of such dense gas effects on modeling assumptions employed for the closure of the Reynolds-averaged Navier–Stokes equations, with focus on the eddy viscosity and turbulent Prandtl number models. For that purpose, we use recent direct numerical simulation results for supersonic turbulent channel flows of PP11 (a heavy fluorocarbon representative of dense gases) at various bulk Mach and Reynolds numbers to carry out a priori tests of the validity of some currently-used models for the turbulent stresses and heat flux. More specifically, we examine the behavior of the modeled eddy viscosity for some low-Reynolds variants of the $k-\varepsilon $ model and compare the results with those found for a perfect gas at similar conditions. We also investigate the behavior of the turbulent Prandtl number in dense gas flow and compare the results with the predictions of two well-established turbulent Prandtl number models.

Hypersonic flow is a very complex regime due to high values of velocity that causes air dissociation and ionization. This paper explores the influence of air dissociation on aircraft aerodynamic properties. The approach is the creation of a block-structured mesh by means of ICEM CFD and further set-up of Fluent solver. Aircraft aerodynamics properties were calculated for cases of perfect gas and non-equilibrium flow. Based on the results of the calculation, a comparison was made between obtained drag pressure coefficients, skin friction coefficients, drag coefficients, lift coefficients, lift-to-drag ratios and pitching moment coefficients.

Steady states of inviscid, compressible and axisymmetric swirling flows of a single-phase, inert, thermodynamically supercritical fluid in a rotating, finite-length, straight, long circular pipe are studied. The fluid thermodynamic behaviour is modelled by the van der Waals equation of state. A nonlinear partial differential equation for the solution of the flow streamfunction is derived from the fluid equations of motion in terms of the inlet flow specific total enthalpy, specific entropy and circulation functions. This equation reflects the complicated, nonlinear thermo-physical interactions in the flows, specifically when the inlet state temperature and density profiles vary around the critical thermodynamic point, flow compressibility is significant and the inlet swirl ratio is high. Several types of solutions of the resulting nonlinear ordinary differential equation for the axially independent case describe the flow outlet state when the pipe is sufficiently long. The approach is applied to an inlet flow described by a solid-body rotation with uniform profiles of the axial velocity and temperature. The solutions are used to form the bifurcation diagrams of steady compressible flows of real fluids as the inlet swirl level and the centreline inlet density are increased at a fixed inlet Mach number and temperature. Focus is on heavy-molecule fluids with low values of $R/C_{v}$. Computed results provide theoretical predictions of the critical swirl levels for the exchange of stability of the columnar state and for the appearance of non-columnar states and of vortex breakdown states as a function of inlet centreline density. The difference in the dynamical behaviour between that of a calorically perfect gas and of a real gas is explored. The analysis sheds new fundamental light on the complex dynamics of high-Reynolds-number, compressible, subsonic swirling flows of real gases.

Aerothermodynamic environment predictions play an important role in the heatshield design of Mars entry vehicle. This article investigates and presents the influences of geometric parameters of the heatshield on its aerothermodynamic performances. The three-dimensional coupled implicit compressible Reynolds Averaged Navier–Stokes (RANS) equations and perfect gas model with the specified effective specific heat ratio have been applied to numerically simulate the flow fields around the vehicle. Menter’s shear stress transport (SST) turbulence model with compressible correction is implemented to take account of the turbulent effect. The laminar and turbulent heating rates are demonstrated and analyzed in detail. Furthermore, a non-intrusive polynomial chaos (NIPC) method with Latin hypercube sampling (LHS) is utilized to establish the functional relationship between the aerothermodynamics and geometric parameters. In addition, Sobol indices as global sensitivity metrics have been introduced to investigate the relative contribution of each geometric parameter. The results show that for the maximum heat flux, the value of the cone angle (αc) with a high index is the top contributor to the both laminar and turbulent flow state, thus the geometric parameter αc should be considered firstly in the material design process of thermal protection system. Moreover, in the most region of MSL heatshield, cone angle (αc) also became the major influence factor. However, in a relatively small region, aerothermodynamics exhibits a great sensitivity to the change of nose radius (Rn). In all regions of heatshield, the parameter of shoulder radius (Rs) is always at a low level of Sobol index.

We consider a gas-dynamic model of a one-dimensional flow of non-viscous perfect gas in the absence of heat conduction when a high-power localized heat source is switched on. Within the framework of this model, it is possible to thoroughly analyze the problem of the gas-flow regimes, which occur as a result of switch-on of such a source, in a wide range of values of the energy-deposition power and initial gas-dynamic characteristics of the flow. Eventually, we obtain a sufficiently general insight into the character of the resulting flows and the conditions of their realizations.

In order to obtain the standing conditions and stationary range of oblique detonation wave in methane-air combustible mixture, we use the Newton-Raphson iteration method to solve the perfect gas flow conservation equations of oblique detonation wave based on detonation theory. We investigate the variation laws of the oblique detonation stationary window and internal mechanism under different methane-air equivalence ratio, incoming flow velocity, initial pressure and initial temperature. The oblique detonation polar curve can be separated into three sections, each of which has different flow characteristics corresponding to different wave morphology. Among them, a stationary oblique detonation wave can be formed when the wedge angle is larger than the wedge angle of Chapman-Jouguet state oblique detonation wave, and smaller than the maximum wedge angle corresponding to the oblique detonation wave without detached. The wedge angle range is called the stationary window of the oblique detonation wave. We found that the oblique detonation is more easily formed when the methane-air mixture is under the oxygen-enriched condition, and the range of oblique detonation wave stationary window becomes larger as the incoming velocity increases. The changes of initial pressure and temperature have little influence on the stationary window. The change law of the stationary window of oblique detonation wave corresponds to the change law of Mach number behind CJ oblique detonation wave. In addition, the standing conditions are mainly related to the coupling of the incoming mixture kinetic energy and heat release.

By using the model of an ideal inviscid perfect gas, the aerodynamic characteristics of a cylinder immersed in a stationary three-dimensional supersonic flow in the case of strong axisymmetrical blowing of air from the lateral surface into the shock layer (“fluid flare”) are investigated. The aim of the present work is to compare the dependences of the aerodynamic characteristics of the cylinder with a “fluid flare” on the angle of attack on increase of the latter from zero to 10o(straight motion) and on its further decrease from 10° to zero (backward motion).

Three continuum models extending the conventional Navier–Stokes–Fourier approach for modeling the shock wave structure in carbon dioxide are developed using the generalized Chapman–Enskog method. Multi-temperature models are based on splitting multiple vibrational relaxation mechanisms into fast and slow processes and introducing vibrational temperatures of various CO2 modes. The one-temperature model takes into account relaxation processes through bulk viscosity and internal thermal conductivity. All developed models are free of limitations introduced by the assumptions of a calorically perfect gas and constant Prandtl number; thermodynamic properties and all transport coefficients are calculated rigorously in each cell of the grid. Simulations are carried out for Mach numbers 3–7; the results are compared with solutions obtained in the frame of other approaches: multi-temperature Euler equations, model kinetic equations, and models with constant Prandtl numbers. The influence of bulk viscosity and Prandtl number on the fluid-dynamic variables, viscous stress, heat flux, and total enthalpy is studied. Bulk viscosity plays an important role in sufficiently rarefied gases under weak deviations from equilibrium; in multi-temperature models, non-equilibrium effects are associated with slow relaxation processes rather than with bulk viscosity. Using a constant Prandtl number yields over-predicted values of the heat flux. Contributions of various energy modes to the total heat flux are evaluated, with emphasis on the compensation of translational–rotational and vibrational energy fluxes.

To investigate the influence of the real-gas effect on the flow of the inward-turning inlet while an air-breathing propulsion system flies at a high Mach number, gas models of thermally perfect gas, chemical non-equilibrium gas, and thermochemical non-equilibrium gas are used for numerical simulation of the inward-turning inlet at Mach 12. The results show that the dissociation reaction is the most severe in the initial stage of the stream-wise vortex and the attachment area of the slip-line near the symmetry plane. The degree of the dissociation reaction in thermochemical non-equilibrium gas is more severe than in chemical non-equilibrium gas. In the thermochemical non-equilibrium gas model, the dissociation degree of oxygen reaches 54.8% at the symmetry plane, and the vortex area of the isolator exit is the smallest, which makes the performance at the isolator exit different from the other two gas models. The real-gas effect in thermochemical non-equilibrium gas has a more obvious influence on the flow characteristics and performance of the inward-turning inlet at Mach 12.

Curved shock theory (CST) is limited to shock waves in a steady, two-dimensional or axisymmetric (2-Ax) flow of a perfect gas. A unique feature of CST is its use of intrinsic coordinates that result in an elegant and useful formulation for flow properties just downstream of a shock. For instance, the downstream effect of upstream vorticity, shock wave curvature, and the upstream pressure gradient along a streamline is established. There have been several attempts to extend CST, as mentioned in the text. Removal of the steady, 2-Ax, and perfect gas limitations, singly or in combination, requires an appropriate formulation of the shock wave’s jump relations and the intrinsic coordinate Euler equations. Issues discussed include flow plane versus osculating plane, unsteady flow, vorticity, an imperfect gas, etc. The extension of CST utilizes concepts from differential geometry, such as the osculating plane, streamline torsion, and the Serret–Frenet equations.

The presented work is a continuation of the investigation of the influence of an isolated roughness on the laminar-turbulent transition for hypersonic boundary-layer flows. The first part of the in...

The conservation laws and the equations of state for quasi-1D motion of compressible fluid in pipeline are formulated in general form, along with the conservative monotone methods suitable for real (multi-component, multiphase) working fluids. The objective is to present a concise approach to construct a general purpose model of pipeline flow for the applied software package, and to present some validation results. The known achievements on higher order monotone schemes for the hyperbolic conservation laws are applied to solve generalized problems of flow in pipes. Specifically, characteristic-based reconstruction and approximate solution to Riemann problem in Godunov-type schemes are used to incorporate real working fluids’ equations of state into explicit numerical schemes. Preliminary validation of the model and the computer code is done for equation of state of perfect gas as a special case. Shown are the solutions to problems for 2 validation cases: (a) Riemann problem (compared with exact solution) and (b) problem of wave action (compared with the experimental data obtained on a single-cycle installation). The results encourage further generalization and testing the model applied to real and multiphase fluids and for compliant pipes.

Laminar and turbulent heating rates play an important role in the design of Mars entry vehicles. Two distinct gas models, thermochemical non-equilibrium (real gas) model and perfect gas model with specified effective specific heat ratio, are utilized to investigate the aerothermodynamics of Mars entry vehicle named Mars Science Laboratory (MSL). Menter shear stress transport (SST) turbulent model with compressible correction is implemented to take account of the turbulent effect. The laminar and turbulent heating rates of the two gas models are compared and analyzed in detail. The laminar heating rates predicted by the two gas models are nearly the same at forebody of the vehicle, while the turbulent heating environments predicted by the real gas model are severer than the perfect gas model. The difference of specific heat ratio between the two gas models not only induces the flow structure's discrepancy but also increases the heating rates at afterbody of the vehicle obviously. Simple correlations for turbulent heating augmentation in terms of laminar momentum thickness Reynolds number, which can be employed as engineering level design and analysis tools, are also developed from numerical results. At the time of peak heat flux on the +3σ heat load trajectory, the maximum value of momentum thickness Reynolds number at the MSL's forebody is about 500, and the maximum value of turbulent augmentation factor (turbulent heating rates divided by laminar heating rates) is 5 for perfect gas model and 8 for real gas model.

We consider triple configurations of compression shocks in supersonic flows of an inviscid perfect gas. The boundaries of the domain of existence of shock-wave structures of a new type (triple configurations with a negative slope of the reflected shock or negative triple configurations) on a set of flow parameters have been theoretically investigated.

International audience; Most of the pumps working under two phase flows conditions are used in petroleum industry applications, like electrical submersible pumps (ESP) for hydrocarbon fluids, in chemistry, nuclear industries and in agriculture for irrigation purposes as well. Two-phase flows always deteriorate overall pump performances compared with single flow conditions. Several papers have been published aiming to understand flow physics and to model all the main mechanisms that govern gas pocket formation and surging phenomena. These mechanisms depend on the pump type, the impeller geometry, the rotational speed, design and off-design liquid flow rate conditions, the volumetric gas fraction, the fluid properties and the inlet pressure. In the present paper, a review on two phase performances from various centrifugal pumps designs is presented, mainly based on experimental results. The main focus is devoted to detect the significant geometrical parameters that: (1) Modify the pump head degradation level under bubbly flow regime assumption; (2) Allow single stage centrifugal pumps keep working under two-phase flow conditions with high inlet void fraction values before pump shut down, whatever the pump performance degradations and liquid production rates should be. Because most of the published experimental studies are performed on dedicated laboratory centrifugal pump models, most of the present review is based on air-water mixtures as the working fluid with inlet pressures close to atmospheric conditions. The following review supposes that gas phase is considered as a non-condensable perfect gas, while the liquid phase is incompressible. Both phases are isolated from external conditions: neither mass nor heat transfer take place between the phases.

Direct numerical simulations of temporally evolving supersonic turbulent channel flows of thermally perfect gas are conducted at Mach number 3.0 and Reynolds number 4800 for various values of the dimensional wall temperature to study the influence of the latter on the velocity-temperature correlations. The results show that in a fully developed turbulent channel flow, as the dimensional wall temperature increases, there is little change in the mean velocity, but the mean temperature decreases. The mean temperature is found to be a quadratic function of the mean velocity, the curvature of which increases with increasing dimensional wall temperature. The concept of “recovery enthalpy” provides a connection between the mean velocity and the mean temperature, and is independent of dimensional wall temperature. The right tails of probability density function of the streamwise velocity fluctuation grows with increasing dimensional wall temperature. The dimensional wall temperature does not have a significant influence on the Reynolds analogy factor or strong Reynolds analogy (SRA). The modifications of SRA by Huang et al. and Zhang et al. provide reasonably good results, which are better than those of the modifications by Cebeci and Smith and by Rubesin.

The interference of an impinging plane oblique shock wave with the viscous shock layer on a cylinder has been studied numerically for rarefied-gas flow regimes at the Reynolds numbers 15.5 ≤ ReR,0 ≤ 124 and Knudsen numbers 0.1 ≥ KnR,∞ ≥ 0.012. The calculations have been performed within the framework of the direct simulation Monte-Carlo technique [1] and the Navier-Stokes equations for a perfect gas using the shock capturing method [2]. The principal properties of flow parameters have been studied for five different types of interference at low Reynolds numbers. The differences with respect to the previously investigated interference regimes for high Reynolds numbers have been examined. The comparison analysis of numerical results and experimental data has been provided. It has been found that the local pressure and heat transfer coefficients on the surface of a cylinder may considerably (by a factor of 3.5) exceed the values on the edge stagnation line observed in the absence of interference. The type IV interference pattern observed in continuum flows has not been found in this study.

In this work we investigate the influence of dense gas effects on compressible wall-bounded turbulence. Turbulent flows of dense gases represent a research field of great importance for a wide range of applications in engineering. Dense gases are single-phase fluids with a molecular complexity such that the fundamental derivative of gas dynamics [1], which measures the rate of change of the sound speed in isentropic transformations, is less than one in a range of thermodynamic conditions close to the saturation curve. In such conditions, the speed of sound increases in isentropic expansions and decreases in isentropic compressions, unlike the case of perfect gases. For dense gases, the perfect gas model is no longer valid, and more complex equations of state must be used to account for their peculiar thermodynamic behavior. Moreover, in the dense gas regime, the dynamic viscosity μ and the thermal conductivity λ depend on temperature and pressure through complex relationships. Similarly, the approximation of nearly constant Prandtl number Pr= μ c p / λ is no longer valid. Numerical simulations of turbulent dense gas flows of engineering interest are based on the (Reynolds-Averaged Navier–Stokes) RANS equations, which need to be supplemented by a model for the Reynolds stress tensor and turbulent heat flux. The accuracy of RANS models for dense-gas flows has not been properly assessed up to date, due to the lack of both experimental and numerical reference data. DNS databases [2, 3] are then needed to quantify the deficiencies of existing turbulence models and to develop and calibrate improved ones. In this work we first summarize some recent direct numerical simulation (DNS) results [4] for supersonic turbulent channel flows (TCF) of PP11, a heavy fluorocarbon representative of dense gases, at various bulk Mach and Reynolds numbers. The most relevant effects are represented by non-conventional variations of the fluctuating thermodynamic quantities, compared to perfect gases and a strong decoupling between thermal and dynamic effects almost everywhere in the flow, except in the immediate vicinity of the solid wall. Preliminary considerations about the validity of some currently-used models for the turbulent stresses and heat flux are carried out based on a priori comparisons between the exact terms computed from the DNS and their modeled counterparts.

The paper solves the problem of selecting optimal methods and combining them when performing a complex calculation of all sections of the Laval nozzle. The problem is significant, since different flow modes are realized in different areas of the nozzle and it is impossible to use a single method for the full calculation. Solving the direct problem, parameters in the flow of gas are determined. Solving the reverse problem determine the profile of the Laval nozzle. Profiling is an important applied task for calculating the nozzles of rocket and aircraft engines, or designing experimental turbines. In this paper, we consider a two-dimensional plane axisymmetric flow of an inviscid perfect gas (on the example of dry air). The problem is solved starting with an accelerating subsonic flow via using methods of establishing and finite elements. For subsonic flow found an exact solution (Prandtl-Mayer flow). Solving the problem in a supersonic flow via using proximate methods (the method of characteristics and interpolation for the grid normalization). The solution is supplemented by a method that allows taking into account the features of axisymmetric flow in the nozzle to expand the applicability of the solution for real nozzles. The results obtained – the gas velocity field and the coordinates of nodes. Results allows estimation of the optimal size of the Laval nozzle for the given conditions, its shape, and obtain a flow profile depending on its initial characteristics defined in the previous section of the nozzle. The results of flow simulation can be applied to calculate the flow in circular sections, which are the most common in the current application. The results are confirmed by the solution using the finite element method, and the convergence of the solution in the diffuser is described in the current work. Theoretically, the solution can be applied to a mixture of gases, if peculiarities of physical and chemical transformations and the participation of combustion products are taken into consideration. In this case instead of parameters in the pre-chamber, the parameters of the combustion chamber and the products in it should be used as initial conditions. This calculation will be carried out in future studies of the authors.

In the case of a variable period (wavelength) of a perturbed interface, the instability and stability of Richtmyer–Meshkov vortices in perfect gas and incompressible perfect fluid, respectively, are investigated numerically and analytically. Taking into account available experiments, the instability of the interface between the argon and xenon in the case of a relatively small period is modeled. An estimate of the magnitude of the critical period is given. The nonlinear (for arbitrary initial conditions) stability of the corresponding steady-state vortex flow of perfect fluid in a strip (vertical periodic channel) in the case of a fairly large period is shown.

This paper proposes a 1-D thermodynamic model for determining the critical pressure ratio, the mixing efficiency and all the dimensions of an optimum ejector providing the highest possible compression ratio for fixed inlet conditions and mass flowrates of the motive and suction fluids. The maximization of the back pressure is obtained subject to constraints imposed by the 2nd law of thermodynamics and the requirements that the flow must be subsonic at the diffuser entrance, that the mixing efficiency must be positive but smaller than one and that the length to diameter ratio for the constant area duct must be between fixed limits recommended in previous studies. The paper also describes a method for determining the off-design performance of a fixed geometry ejector which reproduces the experimental relations between the entrainment ratio, the compression ratio and the inlet conditions of the two fluids. The model uses a fixed polytropic efficiency (rather than the fixed isentropic efficiency used in previous studies) to simulate the acceleration and deceleration processes thus taking into account the effect of the pressure ratio during off-design operation. Examples of its application for isentropic and irreversible acceleration/deceleration of a perfect gas are provided and their results are analysed and compared.

The interaction of shock waves with a turbulent boundary layer on a sharp plate and a blunted plate is numerically investigated. The shock waves in the flow are generated by wedges installed on the flat plate. The flow is simulated by the dynamic equations of a viscous perfect gas. The effect of the blunting radius of the plate’s leading edge and the wedge angle on the flow field and the local aerodynamic coefficients is shown. The calculated results are in agreement with the experimental data.

Axisymmetric acoustic wave propagating in a shear pipeline flow confined by a rigid wall is studied in the two-part paper. The effects of viscous friction and thermal conduction on the acoustic wave propagating in the liquid and perfect gas are respectively analyzed under different configurations of acoustic frequency and shear mean flow. In Part 2 of this paper, comprehensive analysis of the effects of shear mean flow and acoustic frequency on the features (relative phase velocity and attenuation coefficient) of the acoustic wave are numerically addressed in cases of water and perfect gas respectively. Comparisons between the non-isentropic and isentropic models are provided in details. Meanwhile, discussions of the thermoviscous effects on the acoustic wave between water and perfect gas are given.

This article presents a unified approach to solve steady-state conjugate heat-transfer problem including simultaneously gas, liquid and solid regions in just one 3D domain, distinguished by their particular properties. This approach reduces approximation errors and the time to solve the problem, which characterise iterative methods based on separated domains. The formulation employs RANS equations, realisablek-ε turbulence model and near-wall treatment model. A commercial CFD code solves the pressure-based segregated algorithm combined with spatial discretisation of second order upwind. The problem consists of a convergent-divergent metallic nozzle that contains cooling channels divided in two segments along the wall. The nozzle wall insulates the high-speed hot air flow, dealt as perfect gas, from the two low-speed cold water flows, dealt as compressed liquid, both influenced by transport properties dependent of the local temperature. The verification process uses three meshes with increasing resolutions to demonstrate the independence of the results. The validation process compares the simulation results with experimental data obtained in high-enthalpy wind tunnel, demonstrating good compliance between them. Results for the bulk temperature rise of the water in the second cooling segment of the nozzle showed good agreement with available experimental data. Numerical simulations also provided wall temperature and heat flux for the gas and liquid sides. Besides, distribution of temperature, pressure, density and Mach number were plotted along the nozzle centerline showing a little disturbance downstream the throat. This phenomenon has been better visualised by means of 2D maps of those variables. The analysis of results indicates that the unified approach herein presented can make easier the task of simulating the conjugate convection-conduction heat-transfer in a class of problems related to regeneratively cooled thrust chambers.